Morovic and Luo give a comprehensive overview on gamut mapping algorithms. Montag and Fairchild as well as Zolliker present comprehensive comparisons and evaluate different approaches. See notably the following references:    J. Morovic and M. R. Luo, “The Fundamentals of Gamut Mapping: A Survey”, Journal of Imaging Science and Technology, 45/3:283-290, 2001.    Montag E. D., Fairchild M. D, “Psychophysical Evaluation of Gamut Mapping Techniques Using Simple Rendered Images and Artificial Gamut Boundaries”, IEEE Trans. Image Processing, 6:977-989, 1997.    P. Zolliker, M. Dätwyler, K. Simon, On the Continuity of Gamut Mapping Algorithms, Color Imaging X: Processing, Hardcopy, and Applications. Edited by Eschbach, Reiner; Marcu, Gabriel G. Proceedings of the SPIE, Volume 5667, pp. 220-233, 2004.
An application area of color gamut mapping is notably video content production and post-production. For example, an original version of a video content needs to be converted into specific versions adapted for different types of reproduction or transmission: for example, a specific version for cinema, another for television, and a third one for internet. These different versions can be prepared by manual color correction or/and by application of gamut and tone mapping algorithms.
Among the requirements for color gamut mapping are notably:                preservation of color neighborhood and order, absence of color banding and false contours, in order, notably, to prevent from incoherent reproduction of grey and color ramps;        continuity of color and absence of visible quantization or clipping errors, in order, notably, to prevent from banding and false contours;        separate control for lightness, hue and saturation for keeping the full artistic control on how colors are modified, and for allowing the formulation of a higher, semantic level of artistic intents.        
In order to define a color gamut mapping, a gamut boundary description (GBD) of the source color gamut and of the target color gamut is generally used. Such a GBD of a color gamut defines the boundary surface of this color gamut in a color space. GBDs comprise generally explicit, generic 3D representations such as triangle meshes or volume models. For instance, a GBD of a color gamut can be based on a mesh of triangles, each triangle being defined by its three vertices in the color space of this GBD. These vertices are colors located on the boundary of the color gamut.
FIG. 1 illustrates a source color gamut in a RGB color space of a color device. Such a color device can be for instance a display device or an image capture device, or a virtual device corresponding for instance to a standard, as BT.709. This source color gamut forms a cube having vertices formed by a black and white point, by three primary colors, respectively red, green and blue, and by three secondary colors, respectively yellow, cyan and magenta. Rim colors are colors located on a line linking the black or white point with any of the primary colors. Rim colors form rims shown as solid lines. Cusp colors are colors located on a line linking any of the primary colors with any of the secondary colors comprising this primary color. Cusp colors form cusp shown as dotted lines. A target color gamut can be represented similarly as a cube in a RGB color space.
FIG. 2 illustrates the same source color gamut and target color gamut in a CIE Lab color space. When represented in polar coordinates (i.e. with a chroma C and a hue h instead of a and b), this color space allows to define 2D constant-hue leaves having axes for lightness and chroma. Rim lines and cusp lines of the source and target gamuts are shown on this figure.
Still in the Lab color space, FIG. 3 illustrates, in a plane of constant lightness, i.e. in a hue/chroma plane, the projection of the cusp line (solid line) joining the three primary colors Rs, Gs, Bs through the three secondary colors Ys, Cs, Ms of the source color gamut of FIG. 2, together with a projection of the cusp line (dotted line) joining the three primary colors RT, GT, BT through the three secondary colors YT, CT, MT of the target color gamut of FIG. 2. The point at the center of this figure corresponds to the black point and to the white point of FIG. 1.
FIG. 4 shows an exemplary plot diagram illustrating chroma mapping gain in function of hue angle resulting from a color gamut mapping (FIG. 4 will further illustrate an embodiment of the invention—see below). As used herein, the chroma mapping gain may be defined for each hue as the ratio between the chroma of a cusp color at the boundary of the target color gamut and the chroma of a cusp color having the same hue at the boundary of the source color gamut.
The vertical axis of the plot diagram pertains to a chroma mapping gain. The horizontal axis of the plot diagram pertains to hue measured in degrees. The plot diagram includes a plot line that demonstrates the chroma mapping gain versus hue. Plot line relates to mapping the source color gamut to the target color gamut (using a cusp mapping).
In the situation illustrated on this FIG. 4, the chroma mapping gain (γ) is representative of a simple linear chroma mapping which, for each hue, linearly maps the chroma of any source color so that the chroma of the source cusp color having the same hue as said source color is mapped to the chroma of the target cusp color having the same hue in the target color gamut: C′=γ·C. This is a linear function.
Despite the simple definition of this chroma mapping, interpolating this linear function (i.e. interpolating the single coefficient) over a range of hues including a source or a target primary color requires the use of a polynomial function (with hue as variable) with high degree. But even with high degree polynomial functions, interpolation errors are still huge.
These errors are even more critical because they occur for the primary colors which are the most saturated colors. These errors will either lead to clipping or to desaturated colors.
These slope discontinuity points also increase the oscillations of the mapping function (similarly to the so-called Gibbs phenomenon). These oscillations of the mapping function can generate undesirable oscillations in smooth areas of the mapped picture.
This problem illustrated on a simple linear chroma mapping is even more severe when applied to a more complex chroma mapping (i.e. polynomial function of higher degree of the variable chroma) since the errors on each polynomial coefficient are cumulated.
In an angular hue sector that does not include a slope discontinuity point of the chroma mapping function, small low frequency slope oscillations of the section specific chroma mapping function (e.g. the interpolating polynomial function) can occur. These slope oscillations might not be visible in any mapped picture, however they might alter the chroma of critical colors (e.g. skin tones, or any memory colors of familiar objects). In order to avoid such problem, some specific hues might be used as key hues as explained in the description of the invention below. This ensures a more precise control on the chroma mapping function applied on these colors.